Metal-organic frameworks (MOFs), whose definition has been regularly debated, are a sub-class of coordination polymers (CPs) which may feature both an overall 3D architecture and some degree of porosity. In this context, MOFs based on lanthanides (Ln-MOFs) could find many applications due to the combination of sorption properties and magnetic/luminescent behaviors. Here we report rare examples of 3D Ln-CPs based on anilate linkers, obtained under solvothermal conditions using a heteroleptic strategy. The three compounds of formula [Yb2(μ-ClCNAn)2(μ-F4BDC)(H2O)4]·(H2O)3 (1), [Er2(μ-ClCNAn)2(μ-F4BDC)(H2O)4]·(H2O)4 (2) and [Eu2(μ-ClCNAn)2(μ-F4BDC)(H2O)6] (3) have been characterized by single-crystal X-ray diffraction, thermogravimetric analysis, and optical measurements. Structural characterization revealed that compounds 1 and 2 present an interesting MOF architecture with extended rectangular cavities which are only filled with water molecules. On the other hand, compound 3 shows a much more complex topology with no apparent cavities. We discuss here the origins of such differences and highlight the crucial role of the Ln(III) ion nature for the topology of the CP. Compounds 1 and 2 now offer a playground to investigate the possible synergy between gas/solvent sorption and magnetic/luminescent properties of Ln-MOFs.